Online Prediction of Dyadic Data with Heterogeneous Matrix Factorization

Dyadic Data Prediction (DDP) is an important problem in many research areas. This paper develops a novel fully Bayesian nonparametric framework which integrates two popular and complementary approaches, discrete mixed membership modeling and continuous latent factor modeling into a unified Heterogeneous Matrix Factorization~(HeMF) model, which can predict the unobserved dyadics accurately. The HeMF can determine the number of communities automatically and exploit the latent linear structure for each bicluster efficiently. We propose a Variational Bayesian method to estimate the parameters and missing data. We further develop a novel online learning approach for Variational inference and use it for the online learning of HeMF, which can efficiently cope with the important large-scale DDP problem. We evaluate the performance of our method on the EachMoive, MovieLens and Netflix Prize collaborative filtering datasets. The experiment shows that, our model outperforms state-of-the-art methods on all benchmarks. Compared with Stochastic Gradient Method (SGD), our online learning approach achieves significant improvement on the estimation accuracy and robustness.Comment: 26 pages, 10 figure

Absolute cross-section normalization of magnetic neutron scattering data

We discuss various methods to obtain the resolution volume for neutron scattering experiments, in order to perform absolute normalization on inelastic magnetic neutron scattering data. Examples from previous experiments are given. We also try to provide clear definitions of a number of physical quantities which are commonly used to describe neutron magnetic scattering results, including the dynamic spin correlation function and the imaginary part of the dynamic susceptibility. Formulas that can be used for general purposes are provided and the advantages of the different normalization processes are discussed

Dynamics and Structure of PMN and PZN

A review is given of recent neutron and x-ray scattering studies of the lead-oxide perovskite relaxor systems Pb(Zn1/3Nb2/3)O3-xPbTiO3 and Pb(Mg1/3Nb2/3)O3-xPbTiO3. X-ray measurements by Noheda et al. have established that these two systems exhibit nearly identical phase diagrams in which a rhombohedral-monoclinic-tetragonal structural sequence takes place with increasing PbTiO3 concentration. Recent high-energy x-ray and neutron measurements on single crystals of PZN and PMN-10PT, however, show that the rhombohedral distortions occur only in the outermost 20 - 40 microns, while the bulk of each crystal transforms into a new phase X, which has a nearly cubic unit cell. This situation is very similar to the structural behavior of pure PMN at Tc = 220 K. A simple model has been suggested that correlates phase X to the unique atomic displacements of the polar nanoregions, which are created at the Burns temperature.Comment: conference proceeding for the NATO workshop on Disordered Ferroelectrics. To be published on Ferroelectric

3-D mapping of diffuse scattering in PZN-xPT

High energy (67 keV) x-ray diffuse scattering measurements were performed on single crystals of Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-$x$PbTiO$_3$ (PZN-$x$PT). A novel technique was developed to map out the diffuse scattering distribution in all three dimensions around a large number of Bragg peaks simultaneously, taking advantage of the almost flat Ewald sphere of the high energy x-ray beam. For $x=0, 4.5$, and 8%, the results are very similar, indicating same type of correlations of polarizations in these compounds. Our results show that the diffuse scattering intensity consists of six $$rod-type intensities around reciprocal lattice points. These rod-type intensities are very likely due to condensations of soft optic phonon modes, polarized in the perpendicular$$ directions. A simple model is suggested where these soft phonon modes condense into static \{110\} type planar or ``pancake'' shaped correlations of the in-plane $$ polarizations.Comment: Resolution/color of many figures are greatly reduced. For a higher resolution version, go to http://neutrons.phy.bnl.gov/~neutron/PZN_diffuse_3.pd

The Anomalous Skin Effect in Single Crystal Relaxor Ferroelectric PZN-xPT and PMN-xPT

X-ray and neutron scattering studies of the lead-based family of perovskite relaxors PZN-$x$PT and PMN-$x$PT have documented a highly unusual situation in which the near-surface region of a single crystal can exhibit a structure that is different from that of the bulk when cooled to low temperatures. The near-surface region, or "skin" can also display critical behavior that is absent in the crystal interior, as well as a significantly different lattice spacing. By varying the incident photon energy, and thus the effective penetration depth, x-ray measurements indicate a skin thickness of order 10 $\mu$m to 50 $\mu$m for PZN-$x$PT samples with $0 \le x \le 8$%. Neutron residual stress measurements on a large PMN single crystal reveal a uniform lattice spacing within the bulk, but an increased strain near the surface. The presence of this skin effect has led to incorrect phase diagrams for both the PZN-$x$PT and PMN-$x$PT systems and erroneous characterizations of the nature of the relaxor state.Comment: Review Articl

Phase instability induced by polar nanoregions in a relaxor ferroelectric system

Local inhomogeneities known as polar nanoregions (PNR) play a key role in governing the dielectric properties of relaxor ferroelectrics - a special class of material that exhibits an enormous electromechanical response and is easily polarized with an external field. Using neutron inelastic scattering methods, we show that the PNR can also significantly affect the structural properties of the relaxor ferroelectric Pb(Zn1/3Nb2/3)O3-4.5%PbTiO3 (PZN-4.5%PT). A strong interaction is found between the PNR and the propagation of sound waves, i.e. acoustic phonons, the visibility of which can be enhanced with an external electric field. A comparison between acoustic phonons propagating along different directions reveals a large asymmetry in the lattice dynamics that is induced by the PNR. We suggest that a phase instability induced by this PNR-phonon interaction may contribute to the ultrahigh piezoelectric response of this and related relaxor ferroelectric materials. Our results also naturally explain the emergence of the various observed monoclinic phases in these systems

Single-photon frequency conversion and multi-mode entanglement via constructive interference on Sagnac Loop

Based on constructive interference in Sagnac waveguide loop, an efficient scheme is proposed for selective frequency conversion and multifrequency modes W entanglement via input-output formalism. We can adjust the probability amplitudes of output photons by choosing parameter values properly. The tunable probability amplitude will lead to the generation of output photon with a selectable frequency and W photonic entanglement of different frequencies modes in a wide range of parameter values. Our calculations show the present scheme is robust to the deviation of parameters and spontaneous decay

Understanding and Utilizing Deep Neural Networks Trained with Noisy Labels

Noisy labels are ubiquitous in real-world datasets, which poses a challenge for robustly training deep neural networks (DNNs) as DNNs usually have the high capacity to memorize the noisy labels. In this paper, we find that the test accuracy can be quantitatively characterized in terms of the noise ratio in datasets. In particular, the test accuracy is a quadratic function of the noise ratio in the case of symmetric noise, which explains the experimental findings previously published. Based on our analysis, we apply cross-validation to randomly split noisy datasets, which identifies most samples that have correct labels. Then we adopt the Co-teaching strategy which takes full advantage of the identified samples to train DNNs robustly against noisy labels. Compared with extensive state-of-the-art methods, our strategy consistently improves the generalization performance of DNNs under both synthetic and real-world training noise.Comment: Correspondence to: Guangyong Chen <[email protected]

Superconductivity, Antiferromagnetism, and Neutron Scattering

High-temperature superconductivity in both the copper-oxide and the iron-pnictide/chalcogenide systems occurs in close proximity to antiferromagnetically ordered states. Neutron scattering has been an essential technique for characterizing the spin correlations in the antiferromagnetic phases and for demonstrating how the spin fluctuations persist in the superconductors. While the nature of the spin correlations in the superconductors remains controversial, the neutron scattering measurements of magnetic excitations over broad ranges of energy and momentum transfer provide important constraints on the theoretical options. We present an overview of the neutron scattering work on high-temperature superconductors and discuss some of the outstanding issues.Comment: 18 pages, to appear as a Current Perspective in J. Magn. Magn. Mate

Blind Image Denoising via Dependent Dirichlet Process Tree

Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorithm to recover the clean image from noisy one with the unknown noise model. To model the empirical noise of an image, our method introduces the mixture of Gaussian distribution, which is flexible enough to approximate different continuous distributions. The problem of blind image denoising is reformulated as a learning problem. The procedure is to first build a two-layer structural model for noisy patches and consider the clean ones as latent variable. To control the complexity of the noisy patch model, this work proposes a novel Bayesian nonparametric prior called "Dependent Dirichlet Process Tree" to build the model. Then, this study derives a variational inference algorithm to estimate model parameters and recover clean patches. We apply our method on synthesis and real noisy images with different noise models. Comparing with previous approaches, ours achieves better performance. The experimental results indicate the efficiency of the proposed algorithm to cope with practical image denoising tasks.Comment: 25 pages, 11 figure